Electrodynamics of Media

Contains reports on two research projects.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E)M. I. T. Sloan Fund for Basic ResearchNational Science Foundation (Grant GK-3370

Solvable glassy system: static versus dynamical transition

A directed polymer is considered on a flat substrate with randomly located parallel ridges. It prefers to lie inside wide regions between the ridges. When the transversel width $W=\exp(\lambda L^{1/3})$ is exponential in the longitudinal length $L$, there can be a large number $\sim \exp L^{1/3}$ of available wide states. This ``complexity'' causes a phase transition from a high temperature phase where the polymer lies in the widest lane, to a glassy low temperature phase where it lies in one of many narrower lanes. Starting from a uniform initial distribution of independent polymers, equilibration up to some exponential time scale induces a sharp dynamical transition. When the temperature is slowly increased with time, this occurs at a tunable temperature. There is an asymmetry between cooling and heating. The structure of phase space in the low temperature non-equilibrium glassy phase is of a one-level tree.Comment: 4 pages revte

Fractals and dynamical chaos in a random 2D Lorentz gas with sinks

Two-dimensional random Lorentz gases with absorbing traps are considered in which a moving point particle undergoes elastic collisions on hard disks and annihilates when reaching a trap. In systems of finite spatial extension, the asymptotic decay of the survival probability is exponential and characterized by an escape rate, which can be related to the average positive Lyapunov exponent and to the dimension of the fractal repeller of the system. For infinite systems, the survival probability obeys a stretched exponential law of the form P(c,t)~exp(-Ct^{1/2}). The transition between the two regimes is studied and we show that, for a given trap density, the non-integer dimension of the fractal repeller increases with the system size to finally reach the integer dimension of the phase space. Nevertheless, the repeller remains fractal. We determine the special scaling properties of this fractal.Comment: 40 pages, 10 figures, preprint for Physica

Non-Markovian stochastic Liouville equation and anomalous relaxation kinetics

The kinetics of phase and population relaxation in quantum systems induced by noise with anomalously slowly decaying correlation function P (t) ~ (wt)^{- alpha}, where 0 < alpha < 1 is analyzed within continuous time random walk approach. The relaxation kinetics is shown to be anomalously slow. Moreover for alpha < 1 in the limit of short characteristic time of fluctuations w^{-1} the kinetics is independent of w. As alpha \to 1 the relaxation regime changes from the static limit to fluctuation narrowing. Simple analytical expressions are obtained describing the specific features of the kinetics.Comment: 7 pages, 2 figure

Dynamics of Annealed Systems under External Fields: CTRW and the Fractional Fokker-Planck Equations

We consider the linear response of a system modelled by continuous-time random walks (CTRW) to an external field pulse of rectangular shape. We calculate the corresponding response function explicitely and show that it exhibits aging, i.e. that it is not translationally invariant in the time-domain. This result differs from that of systems which behave according to fractional Fokker-Planck equations

Preservation and Promotion of Opera Cultural Heritage: The Experience of La Scala Theatre

This paper focuses on music and music-related cultural heritage typically preserved by opera houses, starting from the experience achieved during the long-lasting collaboration between La Scala theater and the Laboratory of Music Informatics of the University of Milan. First, we will mention the most significant results achieved by the project in the fields of preservation, information retrieval and dissemination of cultural heritage through computer-based approaches. Moreover, we will discuss the possibilities offered by new technologies applied to the conservative context of an opera house, including: the multi-layer representation of music information to foster the accessibility of musical content also by non-experts; the adoption of 5G networks to deliver spherical videos of live events, thus opening new scenarios for cultural heritage enjoyment and dissemination; deep learning approaches both to improve internal processes (e.g., back-office applications for music information retrieval) and to offer advanced services to users (e.g., highly-customized experiences)

Diffusion with random distribution of static traps

The random walk problem is studied in two and three dimensions in the presence of a random distribution of static traps. An efficient Monte Carlo method, based on a mapping onto a polymer model, is used to measure the survival probability P(c,t) as a function of the trap concentration c and the time t. Theoretical arguments are presented, based on earlier work of Donsker and Varadhan and of Rosenstock, why in two dimensions one expects a data collapse if -ln[P(c,t)]/ln(t) is plotted as a function of (lambda t)^{1/2}/ln(t) (with lambda=-ln(1-c)), whereas in three dimensions one expects a data collapse if -t^{-1/3}ln[P(c,t)] is plotted as a function of t^{2/3}lambda. These arguments are supported by the Monte Carlo results. Both data collapses show a clear crossover from the early-time Rosenstock behavior to Donsker-Varadhan behavior at long times.Comment: 4 pages, 6 figure

Quantum Noise Limits for Nonlinear, Phase-Invariant Amplifiers

Any quantum device that amplifies coherent states of a field while preserving their phase generates noise. A nonlinear, phase-invariant amplifier may generate less noise, over a range of input field strengths, than any linear amplifier with the same amplification. We present explicit examples of such nonlinear amplifiers, and derive lower bounds on the noise generated by a nonlinear, phase-invariant quantum amplifier.Comment: RevTeX, 6 pages + 4 figures (included in file; hard copy sent on request